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Alois P. Heinz, <a href="/A340412/b340412.txt">Table of n, a(n) for n = 0..1000</a>

G.f.: Product_{j>=1} (1+x^j)^A226875(j).

Cf. A226875.

allocated for Alois P. Heinz

Number of sets of nonempty words with a total of n letters over quinary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 3, 13, 60, 326, 1345, 6228, 29845, 143899, 732765, 3412167, 16623175, 81624325, 400892932, 2018593583, 9773821243, 48292202375, 239383150209, 1186254809797, 5960931333905, 29322695430795, 145800954979162, 726137079681765, 3616351096084351

0,3

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,

add(b(n-j, j, t-1)/j!, j=i..n/t))

end:

g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))

end:

a:= n-> h(n$2, min(n, 5)):

seq(a(n), n=0..32);

Column k=5 of A292795.

allocated

nonn

Alois P. Heinz, Jan 06 2021

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allocated for Alois P. Heinz

allocated

approved